Semi-Infinite Induction and Wakimoto Modules

Details Semi-Infinite Induction and Wakimoto Modules Semi-Infinite Induction and Wakimoto Modules

1997-04-29

arxiv.org/abs/q-alg/9704020v2

Amer. J. Math. 121 (1999), no. 5, 1079-1094

Mathematics

Quantum Algebra

13 pages; an error in the proof of the Semi-infinite Shapiro Lemma corrected

Scientific paper

The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and coinduction to cohomology. We prove a version of the Shapiro Lemma, relating the semi-infinite cohomology of a module with that of the semi-infinitely induced module. A practical outcome of our construction is a simple construction of Wakimoto modules, highest-weight modules used in double-sided BGG resolutions of irreducible modules.

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